A number of major banks are looking to simultaneously settle probes into allegations of foreign-exchange rate-rigging with the UK's Financial Conduct Authority, according to people familiar with the matter.

The banks, which include Barclays and UBS, are aiming to reach individual settlements with regulators that will be announced at the same time, these people say. The timing of any settlement remains in flux, one person familiar with the matter said.

It isn't clear how many banks are involved and how receptive regulators would be to bringing together an array of banks under one omnibus settlement.

After the mortgage crisis in 2007-09, some US bankers suggested an industrywide settlement, but the idea never went far, as prosecutors and regulators preferred to move slowly, one bank at a time, in extracting billion-dollar settlements.

Among banks, executives have grown more reluctant to be the first to settle with regulators, fearing a reaction similar to the backlash Barclays faced in 2012, according to one of the people familiar with the matter. That year, Barclays became the first bank to settle allegations it rigged a major interbank lending rate, drawing outrage from investors and politicians. Several Barclays executives quit amid the criticism.

Regarding the British foreign-exchange probe, the banks' hope is that simultaneously announced settlements will shift the focus away from individual institutions, people familiar with the matter said.

There are a few examples of groups of banks being fined for transgressions. In the US, 10 banks reached a $1.4 billion civil pact with US regulators a decade ago over allegations related to fraudulent stock research. In Europe last year, six financial institutions were fined €1.71 billion by European Union regulators for colluding in an attempt to manipulate key benchmark interest rates.

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Since last year, authorities in the US, Asia and Europe have been probing possible misconduct in the multitrillion-dollar foreign-exchange market, including efforts by traders suspected of manipulation attempts.

Banks are often reluctant to be named side by side with other lenders who may have bent rules more aggressively. Also, during recent probes into rate rigging, US and UK regulators have tended to pursue perceived fraudulent actions by groups of traders inside individual banks rather than collective efforts by lenders to rig rates.

The probe into Libor underscores the challenges regulators faced coordinating their efforts. In 2012, UK regulators probing rate rigging had to play catchup to their US counterparts, who were much further along in their investigations, a fact that initially stoked tensions between the regulators on opposite sides of the Atlantic, The Wall Street Journal previously reported.

Two years after Barclays paid its £290 million fine for attempting to rig Libor, individual bank settlements continue to dribble out. Lloyds Banking Group is expected to settle next in the UK, according to people familiar with the matter.

The Financial Conduct Authority previously said the investigation has led to "unprecedented global cooperation" among the world's financial regulators, including 52 requests related to the foreign-exchange probe that the authority has received from regulators outside the UK. Banks have already suspended or fired dozens of traders and other employees in connection with the probe, which got under way last spring.

While banks can't necessarily control the timing of their settlements with regulators, the incentive for a bank to step out first to be punished is small.

In 2012, the UK regulator fined Barclays £59.5 million as part of a Libor probe, but the amount included a 30% discount for the bank's cooperation. That brought a political and public backlash, however.

The Libor scandal became associated with Barclays, and public anger resulted in the UK regulator pushing for the bank's top management to step down. As a result, Barclays officials are wary about being the first bank to settle allegations of foreign-exchange rate rigging, according to a person close to the bank.

Write to Max Colchester at max.colchester@wsj.com and Chiara Albanese at chiara.albanese@wsj.com